Manin Involutions for Elliptic Pencils and Discrete Integrable Systems
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AbstractWe contribute to the algebraic-geometric study of discrete integrable systems generated by planar birational maps: (a) we find geometric description of Manin involutions for elliptic pencils consisting of curves of higher degree, birationally equivalent to cubic pencils (Halphen pencils of index 1), and (b) we characterize special geometry of base points ensuring that certain compositions of Manin involutions are integrable maps of low degree (quadratic Cremona maps). In particular, we identify some integrable Kahan discretizations as compositions of Manin involutions for elliptic pencils of higher degree.
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1989 ◽
Vol 22
(13)
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pp. L559-L561
2007 ◽
Vol 36
(4)
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pp. 759-775
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2001 ◽
Vol 280
(1-2)
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pp. 37-44
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2020 ◽
Vol 476
(2237)
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pp. 20200036
2005 ◽
Vol 38
(18)
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pp. 3965-3980
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